Computation of Nevanlinna characteristic functions derived from generating functions of some special numbers

Abstract

In the present paper, firstly we find a number of poles of generating functions of Bernoulli numbers and associated Euler numbers, denoted by n(a, B) and n(a, E), respectively. Secondly, we derive the mean value of a positive logarithm of generating functions of Bernoulli numbers and associated Euler numbers shown as m(2 pi, B) and m(pi, E), respectively. From these properties, we find Nevanlinna characteristic functions which we stated in the paper. Finally, as an application, we show that the generating function of Bernoulli numbers is a normal function.